The problem of a mass connected to a spring is analyzed using Newton's 2nd law to reveal the harmonic oscillator differential equation which is then solved for the position, velocity and acceleration of the oscillator as a function of time.  Arguments are made that such solutions are approximately true for any system for which there exists a potential energy minimum, provided the oscillation is small.  Also, it is demonstrated that identical solutions are obtained for a mass hanging from a vertical spring by applying a thoughtful change in coordinate.

Lecture 029: Harmonic Oscillation Part I

Calculus based physics for undergraduate and high school physics students.

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Lecture 103: Derivatives Part II

Capacitance is defined in the context of an arrangement of parallel plates.  The electric field energy per unit volume is also derived.

Lecture 044: Capacitance

The notion of lines of equipotential is introduced and explored.

Lecture 043: Equipotentials

The electric potential between two parallel conducting plates of known surface charge density is discussed in detail.  This example is of particular interest because it is used to illuminate the relationship between force, field, voltage and energy.

Lecture 042: Parallel Conducting Plates

The Electrostatic Potential energy is derived from the work-energy theorem which leads, in turn to our definition of electric potential, the energy per unit charge.

Lecture 029: Harmonic Oscillation Part I

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